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The Apollonian inner metric and uniform domains
Author(s) -
Huang M.,
Ponnusamy S.,
Wang X.,
Sahoo S. K.
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200710092
Subject(s) - quasiconvex function , metric (unit) , mathematics , isotropy , pure mathematics , mathematical analysis , geometry , regular polygon , physics , optics , convex set , operations management , convex optimization , economics
In this paper we characterize uniform domains in terms of the Apollonian inner metric and the j ‐metric, thus providing solutions to two open problems given in [16]. We also discuss the relationships among uniform, A ‐uniform, Apollonian quasiconvex and quasi‐isotropic domains (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)